{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4548f395",
   "metadata": {},
   "source": [
    "虽然名字里写了FFT，但实际并没有用到，只是做一个简单的功率频谱密度估计就已经百度到死了。包括很多细节，都是自己百度不出来就问磊宝的，现在磊宝已经躲着我走了，所以勉强完成到这种程度"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b07d162",
   "metadata": {},
   "source": [
    "创建一个含 N(0,1) 加性噪声的 100 Hz 正弦波信号。采样频率为 1 kHz。信号长度为 1000 个采样点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a309ade9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import signal as signal\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pylab import mpl\n",
    "rng = np.random.default_rng()\n",
    "mpl.rcParams['font.sans-serif'] = ['SimHei']   #显示中文\n",
    "mpl.rcParams['axes.unicode_minus']=False       #显示负号\n",
    "\n",
    "import numpy as np\n",
    "t = np.linspace(0,1,1000)\n",
    "y = np.sin(2*np.pi*10*t)+np.random.rand(1000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "086e0b0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1fdfa0a0ee0>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "521d94b8",
   "metadata": {},
   "source": [
    "计算并绘制功率谱密度。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "14113b7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, Pxx_den = signal.welch(y,1000)\n",
    "plt.plot(f, Pxx_den)\n",
    "\n",
    "plt.xlabel('frequency [Hz]')\n",
    "plt.ylabel('PSD [V**2/Hz]')\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
